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Sandwich

Sandwich->bread

Get the bread field from a sandwich.

Signature
(sandwich->bread x) → bread
Arguments: x — Guard (sandwich-p x).
Returns: bread — Type (integerp bread).

This is an ordinary field accessor created by defprod.

Definitions and Theorems

Function: sandwich->bread$inline

(defun sandwich->bread$inline (x)
  (declare (xargs :guard (sandwich-p x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'sandwich->bread))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x)))
           (ifix (cdr (std::da-nth 0 x))))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: integerp-of-sandwich->bread

(defthm integerp-of-sandwich->bread
  (b* ((bread (sandwich->bread$inline x)))
    (integerp bread))
  :rule-classes :rewrite)

Theorem: sandwich->bread$inline-of-sandwich-fix-x

(defthm sandwich->bread$inline-of-sandwich-fix-x
  (equal (sandwich->bread$inline (sandwich-fix x))
         (sandwich->bread$inline x)))

Theorem: sandwich->bread$inline-sandwich-equiv-congruence-on-x

(defthm sandwich->bread$inline-sandwich-equiv-congruence-on-x
  (implies (sandwich-equiv x x-equiv)
           (equal (sandwich->bread$inline x)
                  (sandwich->bread$inline x-equiv)))
  :rule-classes :congruence)